Network Interfacial Dynamics of Microstructure Evolution

Modeling the evolution of microstructure in heterogeneous materials requires an efficient computational description of complex interfaces that delineate crystal domains of uniform or homogeneous properties. The motion and reconfiguration of such interfaces change the extent of the uniform domains, and is known to be responsible for most of the mechanical and physical properties at the macro-scale. Examples of the complex dynamics of interfaces include the dynamics of dislocations during plastic deformation, grain growth dynamics during growth or in response to mechanical loads, the evolution of thin film microstructure during CVD or PVD processes, the kinetics of precipitation involving coalescence of growing phases, the evolution of porosity during sintering and consolidation, etc. The largest challenge in all these fundamental phenomena is the topological reconfiguration of the interfaces, including atomic-level constraints. We present here a new computational method that is based on network and graph theories, where the microstructure is described by a network composed of dynamic sub-networks. Each subnetwork contains vertices or (nodes) and a collection of edges (or segments) that connect pairs of vertices, with all the topological properties associated with the mathematical structure of graphs and hyper-graphs. The implementation of this graph theory based model for parallel computing will be discussed, along with a variety of applications at various length scales for modeling the atomic structure of dislocations during crossslip, plastic deformation in small systems (micro-pillars), and the evolution of grains in polycrystals.